Problem: Simplify the following expression: $ r = \dfrac{-1}{3} - \dfrac{-5x - 2}{-8x} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-8x}{-8x}$ $ \dfrac{-1}{3} \times \dfrac{-8x}{-8x} = \dfrac{8x}{-24x} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-5x - 2}{-8x} \times \dfrac{3}{3} = \dfrac{-15x - 6}{-24x} $ Therefore $ r = \dfrac{8x}{-24x} - \dfrac{-15x - 6}{-24x} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{8x - (-15x - 6) }{-24x} $ Distribute the negative sign: $r = \dfrac{8x + 15x + 6}{-24x}$ $r = \dfrac{23x + 6}{-24x}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-23x - 6}{24x}$